Global well-posedness of the Maxwell-Dirac system in two space dimensions

Details Global well-posedness of the Maxwell-Dirac system in two space dimensions Global well-posedness of the Maxwell-Dirac system in two space dimensions

2010-04-10

arxiv.org/abs/1004.1715v3

Mathematics

Analysis of PDEs

Submitted version. Filled gap in local to global argument. Data norm now depends implicitly on existence time, and there is a

Scientific paper

In recent work, Gr\"unrock and Pecher proved that the Dirac-Klein-Gordon system in 2d is globally well-posed in the charge class (data in $L^2$ for the spinor and in a suitable Sobolev space for the scalar field). Here we obtain the analogous result for the full Maxwell-Dirac system in 2d. Making use of the null structure of the system, found in earlier joint work with Damiano Foschi, we first prove local well-posedness in the charge class. To extend the solutions globally we build on an idea due to Colliander, Holmer and Tzirakis. For this we rely on the fact that MD is charge subcritical in two space dimensions, and make use of the null structure of the Maxwell part.

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